Seminar: Data Modeling for Optimization with MPL - Oct 2012

Data Modeling for Optimisation

The Database Connection in MPL
The database connection in MPL has the ability to access data from many
different sources, such as:
• Relational Databases
• Excel Spreadsheets
• External Text Files
• Internet
This gives the model developer the flexibility to choose the most efficient
and convenient way to incorporate the data into the model. Among the
data formats that are supported by MPL are:
• Microsoft Access and Excel
• ODBC
• FoxPro/DBase
• SQL Server
• Oracle
• SAP
Copyright © 2012 Maximal Software, Inc. All rights reserved
1


Import Indexes from Database
MPL allows you to import the elements for an index directly from a
database. In the INDEX section, where you define the index, enter the
keyword DATABASE after the assignment symbol (:=) followed by
parentheses containing the table name and the column/field name you
want to import from.
INDEX
depot := DATABASE("Depots","DepotID");

In the above example, MPL will open the database table Depots, locate
the column DepotID, and then read in the entries for the index depot.

2


Import Indexes from Database
In most cases the imported indexes are the key fields for the table which
are underlined in the following examples:

The Depots Table DepotID Capacity

Atlanta 400000
Chicago 50000
New York 70000
Dallas 100000

The column name defaults to the name of the index so if it is the same you
do not have to specify it. In the example below the column name in the
database table is DepotID which is the same as the index DepotID.
INDEX
DepotID := DATABASE("Depots");

3


Import Indexes from Database (Cont.)
MPL can import from more than one database in the same run. In the
example below, MPL will read in the factory index from Access, instead
of the default database:

INDEX
factory := DATABASE(Access, "Factory", "FactID");

4


MPL also allows you to import subset indexes from database tables.
INDEX
FactoryDepot[factory,depot] := DATABASE("FactDep");

This statement will open the database table FactDep and locate the
columns for factory and depot and then read in the entries for
FactoryDepot.
FactID DepotID TrCost Shipment
The FactDep Table:
Houston Chicago 3200 0
Houston Dallas 5100 0
Seattle Atlanta 2800 0
Seattle Chicago 6800 0
Seattle New York 4700 0
Seattle Dallas 5400 0

Notice that MPL automatically uses the same name as default for the
columns FactID and DepotID, as in the original tables the indexes were
defined from.
5


If an index column does have a different name than in the original table, you
can specify it following the table name by first entering the index name followed
by an equal sign and the column name.
INDEX
FactoryDepot[factory,depot] :=
DATABASE("FactDep", factory="Factory", depot="Depot");

This means if you are consistent in naming the columns in different tables you
do not have to specify them each time you refer to them in MPL.

6


Import Data Vectors from Database
MPL allows you import the elements for a data vector directly from a database.
In the DATA section, where you define the data vector, enter the keyword
DATABASE after the assignment symbol (:=), followed by parentheses
containing the table name and the column/field name you want to import from.
DATA
FactDepCost[factory,depot] := DATABASE("FactDep", "TrCost");

In the above example, MPL will open the database table FactDep, locate the
columns TRCost, FactID, and DepotID, and then read in the entries for the data
vector FactDepCost.

The FactDep Table: FactID DepotID TrCost Shipment

7


Import Data Vectors from Database (Cont.)
If an index column does have a different name than in the original table,
you can specify it following the table name by first entering the index
name, followed by an equal sign and the column name.
DATA
FactDepCost[factory,depot] :=
DATABASE("FactDep","TrCost",factory="Factory",depot="Depot");

The column name defaults to the name of the data vector, so if it is the
same you do not have to specify it.
DATA
TrCost := DATABASE("FactDep");

8


Import Data Vectors from Database (Cont.)
MPL can import from more than one database in the same run. The
default database is specified in the Database Options dialog box in
the Options menu. If you need to import a data vector from table in a
database other than the default, you can do so by specifying the
database name before the name of the table.

In the example below, MPL will read in the data vector DepotCustCost
from Access instead of the default database.
DATA
DepotCustCost := DATABASE(Access, "DepCust", "TrCost");

9


Export Variable Values to Database
After optimizing the problem, MPL can export the variable values to the
database where it can be used to report the solution back to the user. In
the DECISION VARIABLES section, where you define the variable vector,
enter the keyword EXPORT TO after the defined variable, followed by the
keyword DATABASE and parentheses containing the table name and the
column/field name you want to export to.
DECISION VARIABLES
FactDepShip[factory,depot]
EXPORT TO DATABASE("FactDep", "Shipment");

In the above example, MPL will open the database table FactDep, locate
the columns Shipment, FactID, and DepotID, and then export the solution
values for the variable vector FactDepShip.

10


Export Variable Values to Database (Cont.)
Here is an example of the FactDep table after the solution values have
been exported.
The FactDep Table:

FactID DepotID TrCost Shipment


Notice that MPL automatically uses the same name as the default for the
index columns FactID and DepotID, as in the original tables the indexes
were defined from.

11


MPL also allows you to export variable values other than the activity. You
can export the reduced costs, the upper and lower ranges for the objective
function, as well as the objective function coefficient values. You can change
which values will be exported by entering one of the following keywords directly
after the keyword EXPORT: Activity, ReducedCost, ObjectCoeff, ObjectLower,
ObjectUpper.

For example, if you want to export the reduced cost for a variable enter the
following:
DECISION VARIABLES
EXPORT ReducedCost TO DATABASE("FactDep", "ReducedCost");

If you need to export more than one value for a variable vector you can do
so by entering multiple export statements after the variable definition.

12


MPL offers three different options on how the database table is updated
by the EXPORT statement.
• UPDATE, which is the default, searches through the database and for
each record locates the corresponding value in the solver solution and
updates the database entry with it. This option minimizes the changes
done to the database table since only the existing values are updated,
but can sometimes be slow especially on SQL type databases.
• REFILL keyword right after the EXPORT keyword is used to specify
that the whole database table should be emptied and then refilled with
the entries from the solver solution. Since this takes out the necessity
to search the table this can often lead to faster export times for larger
tables.
• CREATE keyword right after the EXPORT keyword is used to specify
that the database table should be created and then filled with the
entries from the solver solution. This option is mainly useful when
exporting to the database table for the first time.

13


Export Constraint Values to Database
Just as exporting variable values, MPL can also export the constraint values
to the database. You will need to define constraint vectors in the
CONSTRAINTS section with the keyword EXPORT TO followed by the
keyword DATABASE and parentheses containing the table name and the
column/field name you want to export to.
SUBJECT TO
FactoryCapacity[factory]
EXPORT ShadowPrice TO DATABASE("Factory", "ShadowPrice");

In the above example, MPL will open the database table Factory, locate the
columns FactID and ShadowPrice, and then export in the shadow price
values for the constraint FactoryCapacity.

14


Export Constraint Values to Database (Cont.)
Here is an example of the Factory table after the shadow price values have
been exported.
FactID Capacity ShadowPrice
120.938
Houston 320000
4
Seattle 73000
0.0000

Notice that MPL automatically uses the same name as the default for the
index column FactID, as in the original tables the factory index was defined
from. If an index column does have a different name than in the original
table you can specify it by first entering the index name followed by an
equal sign and the column name.
SUBJECT TO
EXPORT ShadowPrice TO DATABASE("Factory", "ShadowPrice”, factory="Factory”);

This means, if you are consistent in naming the columns in different tables,
you do not have to specify them each time you refer to them in MPL.
15


Export Constraint Values to Database (Cont.)
In the example below, MPL will export the shadow price of the constraint
vector FactoryCapacity from FoxPro instead of the default database.
SUBJECT TO
EXPORT ShadowPrice TO DATABASE(FoxPro,"Factory","ShadowPrice");

MPL also allows you to export constraint values other than the shadow
price. You can export the slack values, the upper and lower ranges for the
right-hand-side as well as the right-hand-side values. You change which
values will be exported by entering one of the following keywords directly
after the keyword EXPORT: Activity, Slack, ShadowPrice, RhsValue,
RhsLower, RhsUpper. For example, if you want to export the slack for a
constraint enter the following:
SUBJECT TO
EXPORT Slack TO DATABASE("Factory","Slack");

If you need to export more than one value for a variable vector you can do
so by entering multiple export statements after the variable definition.
16


SpreadSheet Modeling in MPL

• Spreadsheet optimisation allows users to create models that are easy
to use, enabling the user to quickly update the data and solve the
model.

• Spreadsheets are efficient at handling and managing 2-Dimensional
dense data and single scalar values.

17


Import Indexes from Excel
MPL allows you to import the elements for an index directly from an
EXCELRANGE. In the INDEX section, where you define the index, enter
the keyword EXCELRANGE after the assignment symbol (:=) followed by
parentheses containing the table name and the column/field name you
want to import from.
INDEX
depot := EXCELRANGE("Depots");

In the above example, MPL will read in the entries for the index depot from
the Excel range called Depots.

18


Import Data Vectors from Excel
MPL allows you import the elements for a data vector directly from EXCEL.
One can read in data in tabular format using the keyword EXCELRANGE or
in sparse format using the keyword EXCELSPARSE, below is an example of
how to import a data vector from EXCEL.
DATA
FactDepCost[factory,depot] := EXCELSPARSE("FactDep", "3");

In the above example, MPL will read in the data vector FactDepCost from the
range called FactDep, as we have specified the data is in sparse format it will
take the first column to be entries for the Factory index, the second column to
be entries for the Depot index and 3 specifies the value of the data parameter
to be taken from the third column.

The FactDep Table: FactID DepotID TrCost Shipment


19


Export Variable Values to Excel
After optimizing the problem, MPL can export the variable values to the
EXCEL where it can be used to report the solution back to the user. In the
DECISION VARIABLES section, where you define the variable vector,
enter the keyword EXPORT TO after the defined variable, followed by the
keyword EXCELRANGE/ EXCELSPARSE and parentheses containing the
range name and the column number if you are using EXCELSPARSE.
DECISION VARIABLES
EXPORT TO EXCELRANGE("Shipping");

In the above example, MPL will export the solution values for the variable
vector FactDepShip to the range called Shipping.

20


Sparse Data vs. Dense Data
• Dense Data
• Standard representation in row and column format
• Row and column format preferably when data is highly dense,
containing none or low percentage of null or zero values
• Can be difficult to deal with for large data sets.
• Sparse Data
• Includes only non zero values
• Highly efficient representation if small percentage of the values
are nonzero
• Efficient. Generating and Solving models

21

Data Modelling for Optimisation

Sparse and Dense Data Examples
Dense Data
In the following example shows the datavector Shipcost. The parameter is
indexed over 4 plants, 2 warehouses and 3 products.
ShipCost[plant, warehouse, product] := [
! p1 p2 p3
{pl1} 70, 52, 48, !w1
65, 40, 74, !w2

{pl2} 79, 52, 65, !w1
75, 50, 53, !w2

{pl3} 47, 52, 51, !w1
78, 52, 52, !w2

{pl4} 75, 80, 50, !w1
90, 52, 10]; !w2

22


Sparse and Dense Data Examples
Sparse Data
The first entry of each row specifies the first index. In our example this
means plant, the second and third entries refers to the machine and
product indexes and the fourth to the actual data value for ProdCost.
ProdCost[plant, machine, product] := [

p1, m11, A1, 73.30,
p1, m11, A2, 52.90,
p1, m12, A3, 65.40,
p1, m13, A3, 47.60,

p2, m21, A1, 79.00,
p2, m21, A3, 66.80,
p2, m22, A2, 52.00,

p3, m31, A1, 75.80,
p3, m31, A3, 50.90,
p3, m32, A1, 79.90,
p3, m32, A2, 52.10,

p4, m41, A1, 82.70,
p4, m41, A2, 63.30,
p4, m41, A3, 53.80];

23


Text vs. Database vs. Spreadsheet

Data can be read in at different speeds depending on the data source.
• Text Files - Are compact and simple and by far the quickest way
to read in data.
• Databases - Are built for data management pretty quick to import
and export data.
• Spreadsheets - Not designed to handle or manage large data sets,
inefficient in importing data and is the slowest method to read in
and export data.

24

Seminar: Data Modeling for Optimization with MPL - Oct 2012

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